Speaker
Pierrick Bousseau, University of Georgia
Abstract
The KSBA moduli space, introduced by Kollár–Shepherd-Barron, and Alexeev, is a natural generalization of “the moduli space of stable curves” to higher dimensions. This moduli space is described concretely only in a handful of situations: for instance, it is shown by Alexeev that the KSBA moduli space of stable toric varieties is also toric variety. Generally, it was conjectured by Hacking-Keel-Yu that the KSBA moduli space of stable log Calabi-Yau varieties is still toric (up to passing to a finite cover). In joint work with Alexeev and Arguz, we prove this conjecture for all log Calabi-Yau surfaces. This uses tools from the minimal model program, log smooth deformation theory, mirror symmetry and punctured log Gromov-Witten theory.